Microsoft argues that 'app store' is a generic term and that Apple shouldn't be allowed to trademark it.

This week, the Redmond, Wash. software giant asked the U.S. Patent and Trademark Office to refuse Apple's request to protect the term, arguing that it's a generic name, like toy store.

"Apple cannot block competitors from using a generic name," Microsoft's lawyers wrote. "'App store' is generic and therefore in the public domain and free for all competitors to use."

Apple's, in turn, argues that the term "App Store" refers exclusively to Apple's online marketplace where it sells its some 300,000 apps.

Apple has been trying to trademark the term "App Store" since 2008, and the application was approved over a year ago. Microsoft, which said it wants to be able to use the term for its own apps offerings, began its fight after the filing became open to appeal.

Shares of Microsoft rose 1.6% to close Wednesday at $28.44, while Apple closed up 0.8% at $344.42.